Theory of groups of finite order [Paperback]

William Burnside (Author)

Book Description

Publication Date: 1955

After introducing permutation notation and defining group, the author discusses the simpler properties of group that are independent of their modes of representation; composition-series of groups; isomorphism of a group with itself; Abelian groups; groups whose orders are the powers of primes; Sylow's theorem; more. 18 illustrations. A classic introduction.

--This text refers to the Hardcover edition.

Product Details

• Paperback: 512 pages
• Publisher: Dover Publications; 2nd edition (1955)
• ASIN: B0007DO4PW
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #3,285,950 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

5.0 out of 5 stars One of the first books devoted to abstract group theory, June 18, 2006

By 

Andreas Klappenecker - See all my reviews
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This review is from: Theory of Groups of Finite Order (Dover Books on Mathematics) (Hardcover)

The "Theory of Groups of Finite Order" by Burnside was first published in 1897 and a second edition in 1911; the Dover Phoenix edition is a reprint of the second edition. The book can be considered as a milestone in the theory of groups. In all prior books (with the exception of Weber's "Lehrbuch der Algebra"), the term group meant "permutation group". Burnside book intended to popularize the notion of an abstract group with the publication of this book.

Groups are defined in the second chapter, after an initial chapter on permutations. The third and fourth chapter discuss the basics of groups, including subgroups, normal subgroups, factor groups, commutators and the derived subgroup. The fifth chapter introduces the composition series of a group, and the sixth chapter discusses the automorphism group of a group. Abelian groups are discussed in chapter seven, and p-groups in chapter eight. The Sylow theorems are discussed in chapter nine. Later chapters are devoted to permutation groups, representations of groups by permutation groups, linear groups, representation theory, and even some infinite groups.

Burnside's book is still very readable, although some of terminology has changes since then. An attractive feature of the book is that it contains many more examples than one typically finds in more recent books on group theory. The exposition is very clear, so that even non-specialists can profit quite a bit. It is rather remarkable how much knowledge was already available one hundred years ago.

The book is not just interesting for historical reasons, but it provides much more examples than more recent books. Overall, I can highly recommend this classic masterpiece.

3 of 3 people found the following review helpful:

3.0 out of 5 stars Good content, lacking in presentation, December 28, 2009

By 

B. Hansberry - See all my reviews
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This review is from: Theory of Groups of Finite Order (Classic Reprint) (Paperback)

I purchased this book as a gift for a mathematician friend. I, myself, am no mathematician and am therefore no authority on the content of the text. My review, instead, concerns the look of the print. While I have no doubt that the content is excellent, I was less than satisfied with the typographical features. While the text was still readable, it was not reset, but has the look of a medium quality photo-copy. This is particularly unfortunate in a mathematics textbook because in some instances subscripts and superscripts become difficult to read.